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On trichotomy of positive singular solutions associated with the Hardy-Sobolev operator. (English. Abridged French version) Zbl 1168.35011
Summary: We present a complete classification of singularities of positive solutions of the equation $$\Delta u + \frac{\mu}{|x|^2}u = h(u)$$ in $$\Omega \setminus \{0\}$$, where $$\Omega$$ is a bounded domain of $$\mathbb R^N$$, $$N\geq 3$$, $$0\in \Omega$$, and $$0<\mu<\frac{(N-2)^2}{4}$$. The case $$\mu =0$$ with $$h(t)=t^q$$, $$q>1$$ were treated by Brezis and Véron.

##### MSC:
 35J60 Nonlinear elliptic equations 35A20 Analyticity in context of PDEs 35A08 Fundamental solutions to PDEs
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##### References:
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